There are many beguiling legends about Pythagoras, one of the most revered of ancient philosophers and a monumental presence in the history of Western thought. According to one account, the Greek philosopher was speaking to followers in a house in his adopted city of Croton when a local faction of men who opposed him came to set the place on fire. Pythagoras’ followers threw themselves into the flames and made a bridge with their bodies for the elderly philosopher to flee.

Such was the devotion to Pythagoras, a man who is alien to the modern mind in many ways. He was both scientist and seer, mathematician and saint. Here was a reconciliation between rationality and transcendent truths, the starting point for both Western science and religion.

Pythagoras, whose fascinating history is described in Kitty Ferguson’s book, The Music of Pythagoras, is best known for the Pythagorean Theorem, which states the square of the hypotenuse of a right triangle is equal to the square of its sides. It is unlikely he was the first to discover this formula, but it was only one of his famous accomplishments, which include discovery of the musical scale. His most profound theory was the idea that mathematical structure underlies all things.

Through his work with the seven-stringed lyre and a single-stringed instrument, Pythagoras, who lived in sixth century B.C., discovered that mathematical ratios undergird harmonies and pitch, forming the basis of what became known as the musical scale. He reasoned that the harmonies of music are the physical expression of abstract relations between and among numbers. From there, he came to the idea that all things are ultimately numerical. All things are relational.

In the Pythagorean scheme, the universe is the physical representation of a divinely rational order. The human soul possesses a natural kinship with all of nature. Unlike the pantheists of our day, who see the soul as harmonious when attuned to itself, the Pythagoreans believed in a moral order external to the self. This natural order is comparable to the perfect triangle never found in real life. It is the ideal for human behavior. Virtue may ultimately lead to immortal perfection. Pythagoras believed in the reincarnation of the soul, but thought the cycle of rebirth could be broken.

In his ethical ideas, Pythagoras foreshadowed the moral philosophies of Plato and Aristotle. Aristotle expressed a Pythagorean truth when he said, “There seems to be in us a sort of affinity to musical modes and rhythms, which makes some philosophers say that the soul is a harmonia, others that it possesses harmonia.”

To a Pythagorean, justice is numerical. Marriage is number. So are masculinity and femininity. The philosopher established a community of followers who lived out his precepts. They were devoted to learning and the virtuous life. Marital fidelity, sexual restraint, kindness toward children, strict rectitude in those who govern – these were among their honored ethical precepts.

Granted, much of what is known about their community is uncertain. The sect observed a code of secrecy. But, it appears to have embodied some of the most enlightened and wholesome ideas about the role of women in Western history. Pythagoras opened his learned society to women, who were free to philosophize and pursue arcane studies. At the same time, Pythagoras did not believe in masculinized women; he perceived the difference in male and female functions.

The Pythagorean community stressed motherhood, believing in the centrality of begetting and raising children, and the practical duties of femininity. One of the greatest of evils was to separate parents from their children. The young Pythagorean woman learned philosophy and literature, but also child-rearing and the domestic arts. Years later, throughout the Greek world, “Pythagorean women” were revered as the greatest exemplars of femininity.

People today often talk about achieving “balance” in a woman’s life, but what they often mean is creating a life that merely fits the most important things in. Balance is a euphemism for doing everything. Balance is disequilibrium, the attempt to walk on a narrow beam though weighted down on one side. It is mathematically incorrect. The very rhythm of our days is mathematical.

The Pythagorean woman may have achieved the true golden mean. She was learned. She was respected for her intellectual potential. But, she never sacrificed for these her fidelity to husband and home. To a Pythagorean, mind is not separate from soul. Our powers of reason are related to our efforts toward virtue. Here is one of the greatest insights of Greek thought. Here is the kernel of Western progress. The true and the good and the beautiful are one.